Suppose that in a fixed population of food consumers, there are just three brands X Y Z that share the market. Suppose that each year,
10% of brand X buyers shift to brand Y and 20% to brand Z and
20% of brand Y buyers shift to brand X and 20% to brand Z
10% of brand Z buyers shift to brand X and none to brand Y
Suppose that it is found that despite all this shifting, the market shares of these brands are nevertheless unchanged, what are these market shares?